Deck 11: The Black-Scholes Formula

Question 1

Suppose the spot exchange rate is $1.43 per British pound and the strike on a dollar denominated pound call is $1.30. Assume r = 0.045, r_f = 0.06, σ = 0.15 and the option expires in 180 days. What is the call option price?

A) $0.133
B) $0.143
C) $0.153
D) $0.163

Answer 1

A

Question 2

Suppose a $60 strike call has 45 days until expiration and pays a 1.5% continuous dividend. Assume S = $58.50, σ = 0.25, and r = 0.06. What is the option elasticity given an immediate price increase of $1.50?

A) 24.61
B) 18.61
C) 14.61
D) 9.61

Answer 2

B

Question 3

What is the price of a $60 strike put? Assume S = $63.75, σ = 0.20, r = 0.055, the stock pays no dividend and the option expires in 50 days?

A) $0.66
B) $0.55
C) $0.44
D) $0.33

Answer 3

C

Question 4

Assume that a $55 strike call has a 1.5% continuous dividend, r = 0.05 and the stock price is $50.00. If the option has 45 days until expiration, what is the vega given a shift in volatility from 33.0% to 34.0%?

A) 0.20
B) 0.15
C) 0.10
D) 0.05

Question 5

Suppose the spot exchange rate is $1.22 per British pound and the strike on a dollar denominated pound put is $1.20. Assume r = 0.04, r_f = 0.05, σ = 0.20 and the option expires in 270 days. What is the put option price?

A) $0.075
B) $0.085
C) $0.095
D) $0.105

Question 6

Assume S = $33.00, σ = 0.32, r = 0.06, div = 0.01. You short 100 $35 strike calls at 68 days until expiration. Under a delta hedge position, what is your overnight profit/loss if the stock rises to $34.50?

A) $9.23 loss
B) $9.23 gain
C) $7.62 loss
D) $7.62 gain

Question 7

What is the delta on a $25 strike put? Assume S = $24.00, σ = 0.35, r = 0.06, the stock pays a 2.0% continuous dividend and the option expires in 40 days?

A) 0.582
B) 0.602
C) 0.662
D) 0.702

Question 8

As the date of expiration approaches, what change in theta might counteract or slowdown the drop in the option price?

A) Decrease
B) Increase
C) Stay constant
D) Indifferent

Question 9

What is the delta on a $20 strike call? Assume S = $22.00, σ = 0.30, r = 0.05, the stock pays a 1.0% continuous dividend and the option expires in 80 days?

A) 0.790
B) 0.820
C) 0.850
D) 0.880

Question 10

Suppose the 120-day futures price on gold is $115.00 per ounce and the volatility is 20.0%. Assume interest rates are 3.5%. What is the price of a $110 strike call futures option that expires in 120 days?

A) $3.09
B) $2.99
C) $2.89
D) $2.79

Question 11

What is the price of a $30 strike put? Assume S = $28.50, σ = 0.32, r = 0.04, the stock pays a 1.0% continuous dividend and the option expires in 110 days?

A) $2.70
B) $2.10
C) $1.80
D) $1.20

Question 12

What is the price of a $25 strike call? Assume S = $23.50, σ = 0.24, r = 0.055, the stock pays a 2.5% continuous dividend and the option expires in 45 days?

A) $0.60
B) $0.50
C) $0.40
D) $0.30

Question 13

Assume that a $60 strike call has a 2.0% continuous dividend, r = 0.05, and the stock price is $61.00. What is the theta of the option as the expiration time declines from 60 to 50 days?

A) -0.52
B) -0.42
C) -0.32
D) -0.22

Question 14

If an investor is speculating with a long call position, what is the most likely preference of the investor, relative to a change in rho?

A) Decrease
B) Increase
C) Stay constant
D) Indifferent

Question 15

Assume that a $75 strike call has a 1.0% continuous dividend, 90 days until expiration and stock price of $72.00. What is the rho of the option as the interest rate changes from 6.0% to 5.0%?

A) 0.07
B) 0.12
C) 0.16
D) 0.20

Question 16

Suppose the 180-day futures price on gold is $110.00 per ounce and the volatility is 20.0%. Assume interest rates are 3.5%. What is the price of a $120 strike call futures option that expires in 180 days?

A) $1.89
B) $2.19
C) $2.59
D) $3.09

Question 17

Assume that an investor is currently holding a reverse straddle position (i.e. a short put and short call), which is currently a profitable investment. All else being equal, what would this investor like to happen to vega?

A) Decrease
B) Increase
C) Stay constant
D) Indifferent

Question 18

What is the total dollar cost to create a delta hedge position against a 200 short call position? Assume calls are priced at $4.16, the delta is 0.7644, and stock price is $73.00.

A) $9,880
B) $10,328
C) $11,168
D) $12,660

Question 19

What is the price of a $35 strike call? Assume S = $38.50, σ = 0.25, r = 0.06, the stock pays no dividend and the option expires in 45 days?

A) $3.50
B) $3.65
C) $3.80
D) $3.95

Question 20

Assume that a $50 strike call has a 3.0% continuous dividend, σ = 0.27, r = 0.06 and 60 days from expiration. What is the gamma for a stock price movement from $48.00 to $49.00?

A) 0.046
B) 0.074
C) 0.089
D) 0.099

Question 21

Which Greek is also called the time decay?

A) Delta
B) Rho
C) Theta
D) Vega

Question 22

What is the difference between implied volatility and historical volatility?

Question 23

A trader who monitors which Greek is most likely to pay close attention to the actions of the Federal Reserve Board?

A) Delta
B) Rho
C) Theta
D) Vega

Question 24

What is the only unobservable variable in the Black Scholes model?

A) Exercise price
B) Interest rates
C) Stock price
D) Volatility

Question 25

What prevents a market-maker from readjusting her delta hedge on a continual basis?

Question 26

Which Greek is also called time decay and why?

Question 27

What is net dollar gain or cost required to create a short put delta hedge against a 100 short put position? Assume puts are priced at $1.98, the delta is 0.489, the stock price is $34.50, and no cost to short stock.

A) $1,540.50 gain
B) $1,540.50 cost
C) $2,319.58 gain
D) $2,319.58 cost

Question 28

What is the difference between a standard bull spread and a calendar bull spread?

Question 29

Draw a payoff diagram for a long put position, depicting options that expire at 0, 30 and 60 days.

Question 30

Assume that a $50 strike put pays a 2.0% continuous dividend, r = 0.07, σ = 0.25, and the stock price is $48.00. What is the profit or loss, per share, for a short put position if the option expires in 60 days and the price rises to $50.00 after 5 days?

A) $1.05 loss
B) $1.05 gain
C) $1.12 gain
D) $1.12 loss

Question 31

Assume S = $33.00, σ = 0.32, r = 0.06, div = 0.01. You short 100 $35 strike puts at 68 days until expiration. Under a delta hedge position, what is your overnight profit/loss if the stock rises to $34.50? Assume no cost to short stock.

A) $8.30 gain
B) $8.30 loss
C) $9.56 gain
D) $9.56 loss

Question 32

Given the following data, what is the approximate implied volatility? Assume S = $38.50, K = $40, r = .06, Call price = $1.60 the stock pays no dividend and the option expires in 45 days.

A) 21 %
B) 32 %
C) 39 %
D) 44 %

Question 33

What Greek will a trader be most interest in if she is buying and selling volatility index options?

A) Delta
B) Rho
C) Theta
D) Vega

Question 34

The Greek that is also called the Hedge Ratio is the .

A) Delta
B) Rho
C) Theta
D) Vega

Question 35

Given the following data, what is the approximate implied volatility? Assume S = $41, K = $40, r = .08, Call price = $2.70 the stock pays no dividend and the option expires in 90 days.

A) 21 %
B) 32 %
C) 39 %
D) 44 %